This work is concerned with the existence of positive weighted pseudo \(S\)-asymptotically periodic solution in Stepanov-like sense for some systems nonlinear delay integral equations. In this context, we will first be interested establishing a suitable composition theorem, and then existing results concerning \(S\)-asymptotic periodicity scalar case are developed here vector case. We point out...

The aim of this work is to provide asymptotic estimates for the splitting of separatrices in a perturbed 3-degree-of-freedom Hamiltonian system, associated to a 2-dimensional whiskered torus (invariant hyperbolic torus) whose frequency ratio is a quadratic irrational number. We show that the dependence of the asymptotic estimates on the perturbation parameter is described by some functions whic...

One of the important advantages held by computer algebra systems (CAS) over purely-numerical computational frameworks is that the CAS can provide a higher-level “symbolic” viewpoint for problem solving. Sometimes this can convert apparently impossible problems to trivial ones. Sometimes the symbolic perspective can provide information about questions which cannot be directly answered, or questi...

In this paper we study the existence of almost periodic solution for nonlinear discrete Volterra equation with unbounded delay, as a discrete version of the results for integro-differential equations. 1. Almost periodic sequences and difference equations Bohr’s theory of almost periodic functions has been extensively studied, especially in connection with differential equations. Almost periodic...

In this study, Palomba economic model was analyzed through difference equations. For these products given as capital and consumer goods in the model, their non-marketable loss rates were also taken into account. Tirivial non-tirivial equilibrium points found local asymptotic stability (LAS) conditions of investigated. Although non-trivial point is always unstable, for trivial found. way, additi...

the main goal of this note is to introduce another second-order differenceequation where every nontrivial solution is of minimal period 5, namelythe difference equation:xn+1 =1 + xn−1xnxn−1 − 1, n = 1, 2, 3, . . .with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

where Aj are linear, closed operators on a Banach space E and f is a function from [0, T ] to E. The asymptotic behavior and, in particular, the periodicity of solutions of the higher order differential equation u(t) = Au(t) + f(t), 0 ≤ t ≤ T, (1.2) has been an subject of intensive study for recent decades. When n = 1, it is well-known [7] that, if A is an n×n matrix on C, then (1.2) admits a u...

We study the large time behaviour of solution linear dispersive partial differential equations posed on a finite interval, when at least one prescribed boundary conditions is periodic. use Q equation approach, pioneered in Fokas & Lenells 2012 and applied to problems half-line van der Weele 2021, characterise necessary for such problem be periodic, an asymptotic sense. then fully describe perio...

Abstract We focus on estimating daily integrated volatility ( IV ) by realized measures based intraday returns following a discrete-time stochastic model with pronounced periodicity (IP). demonstrate that neglecting the IP-impact estimators may lead to invalid statistical inference concerning for common finite number of returns. For given IP functional form, we analytically derive robust IP-cor...